Thesis (M. Sc. (Statistics) / Most social and health science data are longitudinal and additionally multilevel in nature, which means that response data are grouped by attributes of some cluster. Ignoring the differences and similarities generated by these clusters results to misleading estimates, hence motivating for a need to assess variance components (VCs) using multilevel models (MLMs) or generalised linear mixed models (GLMMs). This study has explored and fitted teenage pregnancy census data that were gathered from 2011 to 2015 by the Africa Centre at Kwa-Zulu Natal, South Africa. The exploration of these data revealed a two level pure hierarchy data structure of teenage pregnancy status for some years nested within female teenagers. To fit these data, the effects that census year (year) and three female characteristics (namely age (age), number of household membership (idhhms), number of children before observation year (nch) have on teenage pregnancy were examined. Model building of this work, firstly, fitted a logit gen eralised linear model (GLM) under the assumption that teenage pregnancy measurements are independent between females and secondly, fitted a GLMM or MLM of female random effect. A better fit GLMM indicated, for an additional year on year, a 0.203 decrease on the log odds of teenage pregnancy while GLM suggested a 0.21 decrease and 0.557 increase for each additional year on age and year, respectively. A GLM with only year effect uncovered a fixed estimate which is higher, by 0.04, than that of a better fit GLMM. The inconsistency in the effect of year was caused by a significant female cluster variance of approximately 0.35 that was used to compute the VCs. Given the effect of year, the VCs suggested that 9.5% of the differences in teenage pregnancy lies between females while 0.095 similarities (scale from 0 to 1) are for the same female. It was also revealed that year does not vary within females. Apart from the small differences between observed estimates of the fitted GLM and GLMM, this work produced evidence that accounting for cluster effect improves accuracy of estimates. Keywords: Multilevel Model, Generalised Linear Mixed Model, Variance Components, Hier archical Data Structure, Social Science Data, Teenage Pregnancy